Is there a female or gender-neutral equivalent to the colloquial "man"?

I don't know how to define the usage of man I'm talking about^*, so I'll do it with examples:

Hey, man, what's up?

C'mon, man, don't make me do this.

Is there a female or gender-neutral alternative for this word or is this sort of talk restricted to men only?

_{Is "man" in the examples a normal noun or is it a different grammatical phenomenon, maybe an interjection of sorts?}

In many contexts, you can use there instead of man:

Hey there, what's up?
C'mon there, don't make me do this.

If you're familiar with the addressee and use a friendly or jocular tone, you can often use you in place of man:

Hey you, what's up?

However, it may sound brusque in other contexts, and I wouldn't recommend it with strangers:

C'mon you, don't make me do this.

If addressing a group, you can use folks (if you don't mind sounding a bit folksy):

Hey folks, what's up?
C'mon folks, don't make me do this.

I would say that friend, pal, or mate are used like that and seem pretty neutral to me.

Y'all and guys both work

Hey y'all, what's up?

C'mon, guys, don't make me do this.

I love y'all but I gotta get home.

Listen up, y'all!

Guys can be used for both sexes, if you don't believe me then read this 90+ answer by Caleb here on ELU.

There is a precedent set in Newcastle upon Tyne, where "man" is regularly used, when addressing a male, e.g. "Are yuz gannin oot the neet, man?" (are you going out tonight, my friend?).

In addition, "pet" is often used as an affectionate means of addressing a female. Thus, one might ask "Are yuz gannin oot the neet, pet?" but in order to make that more gender-neutral, and less like "babe" or "hun", one might add "man" to the end, as in "Are yuz gannin oot the neet, pet, man?"

In extreme circumstances, a Geordie (for such is the term for a native of said city) might have already used the word "man" at the end of a sentence, due to it being an oft-used phrase, and so will add "pet" to the end of the sentence to acknowledge to the female that he is aware that he is talking to a female, but will further append another "man" to make the term "pet" seem less like a term of endearment. Hence, you can genuinely hear people say "Are yuz gannin oot the neet, man, pet, man?"

Realistically the most common "equivalent" is to just drop the word. So

"Hey, what's up?"

and

"C'mon, don't make me do this."

Or "Happy Birthday!" instead of "Happy Birthday Man!"

In some circles "girl" is used I would say somewhat equivalently. I would also say this usage tends to be used a little more between women than male to female.